The contrapositive of the following statement, "If the side of a square doubles, then its area increases four times", is
If the area of a square increases four times, then its side is not doubled.
If the area of a square increases four times, then its side is doubled
If the area of a square does not increases four times, then its side is not doubled
If the side of a square is not doubled, then its area does not increase four times
Negation of the statement $P$ : For every real number, either $x > 5$ or $x < 5$ is
Consider the statement : "For an integer $n$, if $n ^{3}-1$ is even, then $n$ is odd." The contrapositive statement of this statement is
The following statement $\left( {p \to q} \right) \to $ $[(\sim p\rightarrow q) \rightarrow q ]$ is
If $p : 5$ is not greater than $2$ and $q$ : Jaipur is capital of Rajasthan, are two statements. Then negation of statement $p \Rightarrow q$ is the statement
Let $p$ and $q$ be two statements.Then $\sim( p \wedge( p \Rightarrow \sim q ))$ is equivalent to